THOG problem

The THOG problem is one of cognitive psychologist Peter Wason's logic puzzles, constructed to show some of the weaknesses in human thinking.

You are shown four symbols

1. a black square
2. a white square
3. a black circle
4. a white circle

and told by the experimenter "I have picked one colour (black or white) and one shape (square or circle). A symbol that possesses exactly one of the properties I have picked, is called a THOG. The black circle is a THOG. For each of the other symbols, are they a) definitely a THOG, b) undecidable, or c) definitely not a THOG?"

Presented in this form, the task is quite difficult, because much information must be held in working memory at the same time. A first step towards a solution is rephrasing the first sentence of the experimenter's statement to "I have picked one of the symbols". It cannot be the black circle, which, being a THOG, possesses only one of the required properties. The chosen properties must describe either the black square or the white circle. The white square, being the "opposite" of the black circle, also has exactly one of the required properties, making it a THOG. The full answer and explanation are as follows: given that the black circle has exactly one of the attributes of the experimenter’s chosen symbol, the chosen symbol must be either the white circle or the black square. If the experimenter’s chosen symbol is the white circle, the white square has exactly one of the attributes of the chosen symbol. If the experimenter’s chosen symbol is the black square, the white square would still have exactly one of the attributes of the chosen symbol. Therefore, the white square is definitely a Thog. If the chosen symbol is the white circle then the white circle has both attributes of the chosen symbol (it is the chosen symbol). If the chosen symbol is the black square then the white circle has zero of the attributes of the chosen symbol. Therefore, the white circle is definitely not a Thog. If the chosen symbol is the white circle then the black square has zero attributes of the chosen symbol. If the chosen symbol is the black square then the black square has both attributes of the chosen symbol (it is the chosen symbol). Therefore, the black square is definitely not a Thog.